Let be any continuous and differentiable function. Find the value of , such that there exists some which satisfies the equation above.
Let denote an function as described above. The number of points where is non-differentiable in is , find .
are the points on the curve
such that the tangents at these points to are perpendicular to the line
Find the value of
Details and Assumptions
denotes the floor function (greatest integer function).
Even though in the problem, a plural form of points is given, there may only be one such point that exists.
What is the largest possible number of integers such that for some fixed polynomial of degree with integer coefficients, ?
Let be a non-constant thrice differentiable function defined on real numbers such that and . Find the minimum number of values of which satisfy the equation Details and Assumptions: